Lawyers for IRA victims seeking compensation from Libya for its role in arming the IRA expressed delight tonight when Gordon Brown promised to send Foreign Office support to back their delegation travelling to Tripoli.

Brown made his offer after he was sharply criticised for refusing to seek a formal agreement between the British and Libyan governments on compensation.

The lead lawyer for the IRA victims, Jason McCue, said he believed the compensation claim could be cleared up within a matter of weeks after securing the prime minister's active support.

"I am overjoyed that the PM has taken a principled decision and overruled the Foreign and Commonwealth Office. He has listened to ordinary folk rather than bureaucrats," McCue said in a statement.

"When we met the PM in December 2008, we knew we had his sympathy; he said he would consider this matter and today he has taken the side of ordinary folk and justice. It is a great day for victims.

"I am confident that his moral and logistical backing for the British victims of Libyan semtex will ensure that they now receive justice and compensation, as did the US victims when they received the support of their president.

"As Libyan diplomats have been reported as saying, the Libyan government is willing to discuss compensation. Now, with our PM's full support, I cannot see why this matter cannot be concluded swiftly in a matter of weeks and before parliament reconvenes."

William Hague, the shadow foreign secretary, described Brown's action as a "stunning admission that the government has failed to support the families of the victims of IRA terrorism in their pursuit of compensation from Libya.

"This U-turn comes only after today's reports that Gordon Brown was personally involved in a decision not to engage Libya on this issue. The British government should have provided active support as a matter of course, not as a result of public pressure. But Gordon Brown and the government he leads have long lost their moral compass and this is just another example of the disastrous mess and muddle in which they find themselves on the Megrahi affair."

Lawyers for the IRA victims had earlier claimed that the prime minister had personally written to them saying he was not prepared to press the Libyan government to provide compensation because of his wider strategy of ensuring the regime renounced terrorism.

Brown said today: "I care enormously about the impact of all IRA atrocities on the victims, their families and friends. Our priority has been to ensure that Libya supports the fight against terrorism and gives up its nuclear weapons.

"As Libya has renounced nuclear weapons and terrorism, our relationship has changed. And as I said last week, it is these concerns – not oil or commercial interests – that have long been the dominant feature of our relationship."

Downing Street has been dogged by the Libyan issue ever since it emerged nearly three weeks ago that it helped pave the way for the Scottish government's independent decision to release the Lockerbie bomber Abdelbaset al-Megrahi. In response to the latest allegations of realpolitik, Downing Street released two letters sent to the IRA victims' lawyers, written last year, showing Brown had turned down their request to seek a new Anglo-Libyan agreement on the issue of compensation. Brown wrote to McCue in October 2008 saying it was not "appropriate" to enter into bilateral talks with Libya on the issue of compensation. He added that Libya would be strongly opposed to reopening the issue.

But Brown argued today that the course most likely to produce results was for the government to actively help the lawyers in representations with the Libyan government. He said: "We will appoint dedicated officers in the Foreign Office and our embassy in Tripoli who will accompany the campaign group to meetings with the Libyan government to negotiate compensation, the first of which will be in the next few weeks."

Brown's October letter also explained that the UK government had lobbied the US government to allow all British victims of Libyan-sponsored IRA terror to pursue compensation in the US courts, but the request had been rejected on largely legal grounds.

The Libyan authorities paid $1.5bn into a US compensation fund in 2003 for the relatives of terror attacks.